IGNOU MTE 10 2018 - The function f (x) = ln(1+ x) is to be tabulated at equispaced points

Question

The function f (x) = ln(1+ x) is to be tabulated at equispaced points in the interval [2, 3] using linear interpolation. Find the largest step size h that can be used so that
the error < 5 x 10^-4 in magnitude.

14 Feb 2018

Answer :

Word Count : 303

To solve this numerically, we need to use the error bound for linear interpolation. The error \(E_L(x)\) in linear interpolation at any point \(x\) is given by: \[ |E_L(x)| \leq \frac{M (b - a)^2}{8n^2} \] where: - \(M\) is the maximum value of the second derivative of \(f(x)\) on the interval \([a, b]\), - \(n\) is the number of intervals, and - \(h = \frac{b - a}{n}\) is the step size. We are given the function \(f(x) = \ln(1 + x)\) on the interval \([a, b] = [2, 3]\). ### Steps: 1. Find the

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